Abstract: A new matrix decoding algorithm for Turbo-codes is derived from Bahl s matrix algorithm. The complex iterating operations are paralleled and well formulclted as a set of simple matrix operations which are fit to design efficient VLSI circuits. Thus, the matrix algorithm increases the decoding speed and simplifies the excessive memory accesses, and is specially fit to Turbo-codes with small memories. States transfer and decoding process of Turbo-codes in 3GPP are also discussed in this paper.